Political scientists often argue that political processes move together in the long run. Examples include partisanship and government approval, conflict and cooperation among countries, public policy sentiment and policy activity, economic evaluations and economic conditions, and taxing and spending. Error correction models and cointegrating relationships are often used to characterize these equilibrium relationships and to test hypotheses about political change. Typically the techniques used to estimate equilibrium relationships are based on the statistical assumption that the processes have permanent memory, implying that political experiences cumulate. Yet many analysts have argued that this is not a reasonable theoretical or statistical assumption for most political time series. In this paper I examine the consequences of assuming permanent memory when data have long but not permanent memory. I focus on two commonly used estimators: the Engle-Granger two-step estimator and generalized error correction. In my analysis I consider the important role of simultaneity and discuss implications for the conclusions political scientists have drawn about the nature, even the existence, of equilibrium relationships between political processes. I find that even small violations of the permanent memory assumption can present substantial problems for inference on long-run relationships in situations that are likely to be common in applied work in all fields and suggest ways that analysts should proceed.